76165 artpubuab driver oai:ddd.uab.cat:76165 articleid 02141493v55n2p475 doi 10.5565/PUBLMAT_55211_10 eng Chung, Daewon Weighted inequalities for multivariable dyadic paraproducts Using Wilson’s Haar basis in Rn, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in Rn. We can then extend “trivially” Beznosova’s Bellman function proof of the linear bound in L2(w) with respect to [w]A2 for the 1-dimensional dyadic paraproduct. Here trivial means that each piece of the argument that had a Bellman function proof has an n-dimensional counterpart that holds with the same Bellman function. The lemma that allows for this painless extension we call the good Bellman function Lemma. Furthermore the argument allows to obtain dimensionless bounds in the anisotropic case. Article de fons article info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Vol. 55, Núm. 2 (2011), p. 475-499 Publicacions Matemàtiques 0214-1493 25 213881 http://ddd.uab.cat/uab/pubmat/02141493v55n2/02141493v55n2p475.pdf 0475 499 2 55 02141493v55n2 2011 ARTPUB PUBMAT UAB Tots els drets reservats http://www.europeana.eu/rights/rr-f/